9y^{''}+6y^'+82y=0,y(0)=2

Lösung

9 y^{^{''}} + 6 y^{^{'}} + 82 y = 0, y (0) = 2

y = e^{- \frac{t}{3}} (2 cos (3 t) + c_{2} sin (3 t))

Schritte zur Lösung

9 y^{''} (t) + 6 y^{'} (t) + 82 y = 0

Solve linear ODE:

y = e^{- \frac{t}{3}} (2 cos (3 t) + c_{2} sin (3 t))

y = e^{- \frac{t}{3}} (2 cos (3 t) + c_{2} sin (3 t))

x^{^{'''}} - 4 x^{^{''}} - 3 x^{^{'}} + 18 x = 0

4 y^{^{''}} - 4 y^{^{'}} + 5 y = 0

y^{^{''}} - 10 y^{^{'}} - y = 0

y^{^{'''}} + 4 y^{^{''}} + 4 y^{^{'}} = 0

x^{^{''}} - x^{^{'}} - 6 x = 0